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Interpretation:
The dihedral angle needs to be determined, for which the interfacial energy of the matrix-precipitate boundary and the grain boundary energy of the matrix will be equal.
Concept introduction:
A dihedral angle is defined as the angle among the two interconnecting planes. The angles between the planes over the two sets of three atoms, which have two atoms in communal. The grain boundary is defined as the border between the two grains, or crystallites which are existing in the polycrystalline material. The grain boundaries are important in various
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Chapter 12 Solutions
Essentials of Materials Science and Engineering, SI Edition
- In the zone refining of silicon, an RF-heater is used to remove trace amounts of impuritiesfrom the silicon. If the silicon has the impurity of 10^14 Co (k = 8*10^-6) what is the purityof the crystal after one pass of the zone refiner? After two passes? Plot concentration as afunction of crystal length from 0 to 8ft (total length of the crystal). The width of the moltenzone is 5”.arrow_forwardQuestion 5 Calculate the Moment about the point B in Nx m B 500 N A 2 m 1.2 m 0.8 m 300 N 7arrow_forwardNot use ai pleasearrow_forward
- 2. Determine the centroid and moment of inertia, lxx. a) 2in x 4in 1in x 4in b) 1/2in plywood metal plate 3/4in x 10in c-channel 10in x 25in Ixi = 92.14in1 Aix = 7.35in² 24inarrow_forwardCan you solve for V1 and V2arrow_forward(1 point) By dragging statements from the left column to the right column below, give a proof by induction of the following statement: an = = 9" - 1 is a solution to the recurrence relation an = 9an-18 with ao = : 0. The correct proof will use 8 of the statements below. Statements to choose from: Note that a₁ = 9a0 + 8. Now assume that P(n) is true for all n ≥ 0. Your Proof: Put chosen statements in order in this column and press the Submit Answers button. Let P(n) be the predicate, "a = 9″ – 1". απ = 90 − 1 = Note that Let P(n) be the predicate, "an 9" - 1 is a solution to the recurrence relation an = 9an-1 +8 with ao = 0." - Now assume that P(k + 1) is true. Thus P(k) is true for all k. Thus P(k+1) is true. Then ak+1 = 9ak +8, so P(k + 1) is true. = 1 − 1 = 0, as required. Then = 9k — 1. ak Now assume that P(k) is true for an arbitrary integer k ≥ 1. By the recurrence relation, we have ak+1 = ak+1 = = 9ak + 8 = 9(9k − 1) + 8 This simplifies to 9k+19+8 = 9k+1 − 1 Then 9k+1 − 1 = 9(9*…arrow_forward
- Solve this problem and show all of the workarrow_forwardGiven that an L-shaped member (OAB) can rotate about OA, determine the moment vector created by the force about the line OA at the instant shown in the figure below. OA lies in the xy-plane, and the AB part is vertical. Express your answer as a Cartesian vector.arrow_forwardyou dont need to solve the question i just wanna know the steps and how to find the angle between the voltage difference and the current . thanks so mucharrow_forward
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